PART 1:

Erin needs to buy a used car so that she can drive to class. Sean has a used Audi that hed like to sell. The car is worthless to Sean but worth $100 to Erin. Sean makes a take-it-or-leave-it offer to sell the car to Erin for $p. Erin observes Seans price and chooses to either accept or reject his proposal. If Erin accepts Seans price, then Seans payoff is p and Erins payoff is 100 p. If Erin rejects Seans offer, then Seans payoff and Erins payoff are both 0.

Question 1:

1. Write down the normal form of this game.

2. State the complete set of prices p that are accepted by Erin as the outcome of some Nash Equilibrium (you only need to describe the equilibrium outcomes, not the entire strategy profile).

3. State the complete set of prices p that are accepted by Erin as the outcome of some Subgame Perfect Nash Equilibrium (you only need to describe the equilibrium outcome, not the entire strategy profile).

PART 2:

The car that Erin bought from Sean isnt in great shape and will require annual maintenance. The local Audi dealership conducts the sort of routine maintenance that Erins car needs for a fixed price of $50. As it happens, Sean works part time as an auto mechanic and offers to fix Erins car. However, Sean doesnt know how long it will take him to work on Erins car, and so the only promise he can make to Erin is that hell match or beat the dealerships price. Sean makes an offer to fix Erins car for price p thats between $0 and $50. Simultaneously and without observing the price p, Erin chooses either to accept or reject. If Erin accepts, her payoff is 50 p and Seans payoff is p. If Erin rejects, both of their payoffs are 0.

Question 2:

Consider the situation described at the top of this page. Suppose that Erin enrolls in a local masters program with a two year duration. She intends to keep the car for the duration of her program and then sell it. Identify the subgame perfect Nash Equilibria of the twice repeated stage game with no discounting.

Question 3: Consider again the situation described at the top of this page. Suppose that Erin enrolls in a local doctoral program with an indefinite duration. Identify conditions on the discount factor under which Sean works on the car every year for $25 as the outcome of a Subgame Perfect Nash Equilibrium in the infinitely repeated stage game with common discount factor . Tip: use grim trigger strategies.